## J

where k = 55 (from Fig. 11 -35), v (Poisson's ratio) = 0.33, r = 1 m, t = 0.127 cm, and b = 0.5236 m (the spacing between stringers). The buckling load, P„ - aCT x area = (21.2 x 106) (0.0180 m2) = 381,000 N. The resulting margin of safety, MS, is

The negative margin of safety points out the inadequacy of the design, so we must add thickness to keep the panel from buckling, resulting in the values shown in Table 11-61. When we increase the thickness like this to prevent panel buckling, we can decrease the area of the stringers, with the goal of achieving the same total area and moment of inertia needed for bending stiffness. With a skin thickness of 0.195 cm, this means the required stringer area is 4.78 cm2.

Table 11-61 summarizes the estimation of mass for the skin-stringer option, using a mass density of 2,800 kg/m3. Note we've included an extra 25% to account for ring frames, which are needed to stabilize the stringers and fasteners; this is simply an estimate. Note also that, in a real sizing exercise such as this, we would need to confirm the feasibility of only 4.78 cm2 area for each stringer. To keep a stringer from buckling as a column between ring frames, we need to design its cross section to have a relatively large moment of inertia. A common strategy for doing this at low mass is to use a thin-walled I- or C-section. However, we might find that, to provide the needed area moment of inertia with an area of 4.78 cm2, we would need to make the flanges and webs so thin that they could not carry the design load without buckling locally. Chapter 8 of Sarafin  explains how to assess column buckling and local buckling for thin-walled structural members.

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